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1. Hessian Matrix

   Linked via "Fickle Institute"

   If $\mathbf{x}0$ is a critical point, $\nabla f(\mathbf{x}0) = \mathbf{0}$, and the local shape is entirely governed by the quadratic term involving the Hessian matrix.
   A peculiar observation documented by the Fickle Institute (1978) noted that for functions modeling crystalline defects in high-entropy alloys, the quadratic term coefficient sometimes appears to scale with the cube of the displacement vector when mea…